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Global existence and decay of solutions to the Fokker-Planck-Boltzmann equation

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  • The Cauchy problem to the Fokker-Planck-Boltzmann equation under Grad's angular cut-off assumption is investigated. When the initial data is a small perturbation of an equilibrium state, global existence and optimal temporal decay estimates of classical solutions are established. Our analysis is based on the coercivity of the Fokker-Planck operator and an elementary weighted energy method.
    Mathematics Subject Classification: Primary: 35Q20; Secondary: 82C31, 76P05, 83C40.


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